Find the quotient and remainder using synthetic division for
1³ + 31² + 8x + 14
------------------------
x + 2
The quotient is
The remainder is
Answers
Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2
Explain equationA mathematical depiction of two equal variables, one on either side of a "equals" sign, is called an equation. Equations can be used to solve common problems. To solve challenges in real life, we frequently turn for pre algebra assistance. Lessons in pre-algebra cover the foundational ideas of mathematics.
Here,
Given : synthetic division for
x³ + 3x² + 8x + 14
------------------------
x + 2
Write the problem in synthetic division format
-2 | 1 3 8 14
-2 -2
------------------------
1 1 6
Carry down the leading coefficient, unchanged, to below the division symbol
-2 | 1 3 8 14
-2 -2
---------------------------
1 1 6
Multiply the carry - down value by the zero of the denominator, and carry the result up into the next column:
1(-2)=-2
-2 | 1 3 8 14
-2 - 2
------------------
1 1 6
=> We get:
As
x² +x+6+ [tex]\frac{2}{x+2}[/tex]
and remainder is 2
Therefore , the solution to the given problem of equation comes out to be quotient : x² +x+6+ [tex]\frac{2}{x+2}[/tex] and remainder is 2.
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Related Questions
In Exercises 10-11, find the range of the function.
10. k(x) = x² + 9
11. f(x) = (x + 5)² +3
Answers
As a result, the answer to the given function question is that the domain and range are both(-∝, ∝) and that the domain is (-∝, ∝).and that the range is(-∝, ∝).
What is function?Any input will only result in one or zero outcomes for the function. The expression does not define the function if there are several outputs for a given input. Each value of x must have only one output value of y variable in order for anything to be a function.
Here,
The formula is presented as
k(x) = x² + 9
The aforementioned equation is linear.
the range is (-∝, ∝) and the domain is(-∝, ∝)
Formula 2
The formula is presented as
y = (x + 5)² +3
The aforementioned equation is linear.
The range is (-∝, ∝), and the domain is (-∝, ∝).
As a result, the answer to the given function question is that the domain and range are both(-∝, ∝) and that the domain is (-∝, ∝).and that the range is(-∝, ∝).
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Solve the exponential equation. 1/16 = 64^4 x − 3
Answers
Answer:
x=7/12Step-by-step explanation:
1/16=64^4x-3
1/4^2=(4^3)^4x-3
4^-2=(4^3)^4x-3
4^-2=4^3*(4x-3)
Since the bases are equal (to 4), the exponents must be equal to each other.
-2=3*(4x-3)
-2=12x-9
-2+9=12x
7=12x
7/12=x
x=7/12
So the answer is x=7/12
Please mark me brainliest if this helped!The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 2.
1. x = -1, y = 29
2. x = 8, y = 11
Answers
1) The equation is:
y = -29/x
And when we evaluate in x = 2, we get y = -14.5
2) The equation is:
y = 88/x
And when we evaluate in x = 2, we get y = 44
How to find the equation between x and y?We know that the variables x and y vary inversely, then the equation between these variables will be something like:
y = k/x
Where k is a constant.
1) First we know that when x = -1, y = 29, replacing these values we will get:
29 = k/-1
-1*29 = k
-29 = k
Then the equation is:
y = -29/x
If now we evaluate in x = 2, we will get:
y = -29/2
y = -14.5
2) Now we know that x = 8 and y = 11, replacing these we get:
11 = k/8
11*8 = k
88 = k
So the equation is:
y = 88/x
If now we replace x by 2, we will get:
y = 88/2 = 44
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What is the solution of the system of equations? Show your work.
4x - 2y = 10
2x + y = -3
Answers
Answer:
no solutions
Step-by-step explanation:
you have to divide the whole first equation by 2 and you would get
2x+y=5
2x+y=-3
That is not true the same thing can’t have different outcomes.
it is no solution
Which point(s) lie on the graph of the equation y = -5x - 3?
Answers
Explanation below in image
Plug in values of x to find corresponding values of y.
For example, replace x with 0 to find that...
y = -5x-3
y = -5*0 - 3
y = 0 - 3
y = -3
We have x = 0 lead to y = -3.
Therefore, the point (0, -3) is on this line. This is the y intercept.
Now try something like x = 1
y = -5x-3
y = -5*1 - 3
y = -5 - 3
y = -8
It shows the point (1,-8) is also on the line.
The straight line goes through (0,-3) and (1,-8)
We can repeat this process infinitely many times since there are infinitely many numbers to pick for x.
See the graph below. I used GeoGebra to make it, but you can use something like Desmos or similar.
Please I need help also please explain your answer and show the work
Answers
1. The degree form of 4π/9 is approximately 228.6°.
2. A positive coterminal angle to -123° that is between 500° and 750° is 677°. A negative coterminal angle to -123° that is between -300° and -500° is -243°.
3. The terminal side of 215° lies in the second quadrant.
4. The radius of the circle is approximately 15.7.
1. The degree form of 4π/9 is approximately 228.6°. To express an angle in degrees, we multiply its radian measure by 180°/π.
2. A positive coterminal angle to -123° that is between 500° and 750° is 677°. A negative coterminal angle to -123° that is between -300° and -500° is -243°. To find a coterminal angle, we can add or subtract 360° as many times as necessary to bring the angle into the desired range.
3.
In the standard position, an angle is measured counterclockwise from the positive x-axis. The positive x-axis corresponds to the 0° angle, the positive y-axis corresponds to the 90° angle, the negative x-axis corresponds to the 180° angle, and the negative y-axis corresponds to the 270° angle. Angles in the first quadrant are between 0° and 90°, angles in the second quadrant are between 90° and 180°, angles in the third quadrant are between 180° and 270°, and angles in the fourth quadrant are between 270° and 360°.
So, the terminal side of 215° lies in the second quadrant.
4.
We can set up the equation l = Cθ/2π and solve for r.
Substituting the given values, we have 56π = (2πr)(120°/180°), which simplifies to r = 56π/(2π) = 28.
Dividing this value by 2, we get the radius of the circle as approximately 15.7.
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any help please — Put the fractions 12,38 and 34 in order from smallest to largest. Find the value of 113+256.
Answers
The value of 113+256 is determined by the above fractional formulae. Is 369
Why are fractional equations difficult to solve?An exact number that shows a percentage of a total is called a fraction. You may figure it out by dividing a sum by the quantity of parts. As an example, the number 12 represents one-half of a whole number or an object. Simple subtraction of the smaller numerator from the larger numerator will yield the solution to the problem. To solve, for instance, 6/8 - 2/8, just take 2 out of the answer. The answer, which can be abbreviated to "4/8," is 12, or 12.
Making a fraction simpler by reducing or simplifying it is our goal. In order to do this, we divide the denominator and numerator by the largest integer that can be divided into both integers precisely. That is to say,
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Write the expression d-7 / 2 in words
Answers
Answer:
The expression "d-7 / 2" can be written in words as
Step-by-step explanation:
The expression "d-7 / 2" can be written in words as "the quotient of d minus 7, divided by 2".
This is the operation of subtracting 7 from d and then dividing the result by 2.
Please help will mark Brainly
Answers
Answer:
371 children
Step-by-step explanation:
289*$2,5 + 371*$1,5 = $1279
The sum of any three different even numbers is odd.
Answers
The sum of three odd numbers is odd same thing goes for three even numbers which would be even but A even number divided by two would leave a remainder of zero
10 POINTS!
What is the constant of proportionality in this proportional relationship?
x 2 4 6 8
y 5/6 1 2/3 2 1/2 3 1/3
A. 12
B. 5
C. 12/5
D. 5/12
Answers
Answer:
d
Step-by-step explanation:
The constant of proportionality in a proportional relationship is the number that relates the two variables, x and y, in the equation y = kx.We can see that the relationship between x and y is in the form of y = kx. We can find the constant of proportionality (k) by dividing the y-value by the corresponding x-value.For example:
x = 2; y = 5/6
k = y/x = (5/6) / 2 = 5/12The constant of proportionality is 5/12 for the given proportional relationship,
y = kx where k = 5/12Note that it is important to understand that the relationship is a proportion because in this case, the k(constant) is the same for every point, if we calculate each (y/x) point it will be 5/12
Are x and y proportional when Y /X equals five
Answers
Answer:
no
Step-by-step explanation:
In a recent year, 22.2% of all registered doctors were female. If there were 47,200 female registered doctors that year, what was the total number of registered doctors?
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Answers
Therefore , the solution of the given problem of percentage comes out to be 264414 doctors were registered that year.
What is a percentage?A% is a number that represents the percentage of 100 that it is, and it can also be stated as a decimal or a fraction. To convert a percentage to a fraction, place 100 in the denominator and the percentage number in the numerator.
Here,
"Female doctors make up 22.2% of all registered doctors," the inquiry states.
Consider the entire number of doctors who are registered as x; 22.2% of those doctors are women.
and 47,200 divided by 22.2% of x
=>22.2/100 * x = 47,200
in math
264414 doctors were registered that year, or
x = 58700* 100/22.2 x.
Therefore , the solution of the given problem of percentage comes out to be 264414 doctors were registered that year.
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Can anyone pls help I need the answer quickly
Answers
Therefore , in response to the given problem of triangle, we can state that the triangles ECD and PQR
Describe the triangle.A triangle is a polygon since it has four segments and three vertices. It is one of the basic geometric forms. The title given to that of a triangle with the vertex A, B, and C is Triangle ABC. A unique planes and trapezoid in Geometric forms are discovered once the three criteria are not collinear. Quadrilateral and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where its three sides converge. 180 degrees is the result of multiplying three triangle angles.
Here,
=> EC = PQ (equal side)
=> CD = PR (equal side)
=> ED = QR (equal side)
as a result, the SSS property compares both triangles.
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Why can’t a nose be 12 inches long Worksheet
Answers
Here are two number machines that always give the same number for any input. Use the machines expressions to explain why both machines will produce the same outputs for any input.
Answers
Timothy bought a house for $360,000. He paid 20% down, and agreed to pay $1,375.69 per month for 30 years. His payment of $1,375.69 does not include property tax and insurance. How much interest will Timothy pay in 30 years?
Answers
INTREST-300000
Step-by-step explanation:
36000000
Solve 2 < n +1| ≤ 7. Explain your reasoning and graph
the solution set.
Answers
Let n = the number
The solution set is {x | x > 10}. 2. 5 ≥ 7 + y.
What is the value of N?It's used to refer to the collection of all natural numbers. Positive whole numbers that are not zero make up the natural numbers. N = 1 , 2 , 3 , 4 . By multiplying the integers from 1 to n, the factorial of n is calculated and denoted by the symbol n!. n! = n (n - 1)! is the formula for n factorial. Example: What is9! if8, which is40,320, is?The sample size, or n, is the number of data points. described in Chapter 2 here. in a probability experiment using a binomial model, the total number of trials.Instead of the product n n, which is typically pronounced"n squared," the equivalent exponentiation n2 is used to represent a number's square.To learn more about exponentiation refer to:
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the set {...,-2,-1,0,1,2...} is called what?
Answers
Answer: Set of integers
Integers are positive and negative whole numbers, with 0 included.
Answer: Set of Integers
Step-by-step explanation:
{...,-2,-1,0,1,2...}
since we can see that here is a zero as well as positive and negative numbers, therefore, we call this set, a set of integers.
hope that helps...
Write 49D2
in the base-ten system.
Answers
Each position in base 10 is worth ten times the place to its right, and there are ten numbers (0–9). 49D2 in the base-ten system is equal to 204064.
What does base-10 value 2 have?When you come to "two," you discover that there isn't a single digit in base-two math that stands for "two." Instead, you enter a "1" for "1 two" and a "0" for "0 ones" in the twos and units columns, respectively.
[tex]49D2 in the base-ten system is 4916^3 + 1316^2 + 216^1 \\\\= (494096) + (13256) + (216) \\\\= 200704 + 3328 + 32\\ \\= 204064[/tex]
Binary has a basis of 2 or 10.A binary counting system simply employs the numerals 0 and 1 in each place. Base 2 is another name for binary. In binary, a second place is required to represent a number greater than 1.
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Need help solving this please
Answers
Answer:
30 students
Step-by-step explanation:
First, we need to find exactly how many students went to school by car and how many went on the bus.
To do this, we simply multiply the fraction of students that used each transportation method by the total number of students.
[tex]\# \textrm{ of students by car} = \dfrac{3}{8} \times 240 = \dfrac{3 \times 240}{8} = \dfrac{720}{8} = 90 \textrm{ students}[/tex]
So, 90 students went to school by car.
[tex]\# \textrm{ of students on bus} = \dfrac{6}{12} \times 240 = \dfrac{1}{2} \times 240 = \dfrac{240}{2} = 120 \textrm{ students}[/tex]
So, 120 students went to school on the bus.
The number of students that walked to school is the same as the number of students who didn't go in a car or on the bus, so to find the number of students that walked to school, we can subtract the number of students that went by car and on the bus from the total number of students.
[tex]\# \textrm{ of students that walked} = 240 - 90 - 120 = 30 \textrm{ students}[/tex]
The fourth term of an arithmetic sequence is 20. The common difference is -1/5 times the first term. What is the first term? Graph the sequence.
Answers
As a result, the first term of the answer to the given arithmetic mean problem is 14.
What does arithmetic mean?The Arithmetic Mean or Average of the Group is the product of the sum of all the numbers in a group and the amount of items in that list, divided by both. The Geometric progression is also same as this .This average of the numbers 5, 7, and 9 is, for instance, 4, as 5 + 7 + 9 is 21, and 21 split by 3 [there really are three numbers] equals 7.
Here,
In this case, t(n) = (a + ((n — 1) * d)),
The value of the nth term is t(n),
The first term of the AS is a.
The position of a value in the A.S. is represented by the positive whole integer n, and
The constant common difference among A.S. words is d.
In light of the question, we can say:
11 = (5 + ((4 — 1) * d)),
Take 5 away from both sides.
11 — 5 = (5 + ((4 — 1) * d)) — 5,
On the RHS, the fives cancel one another out.
6 = 3d,
d = 2.
In summary, the common distinction is: 2.
=> 20 = a + 3d
=> 20 - 6
=> a =14
As a result, the first term of the answer to the given arithmetic mean problem is 14.
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Refer to the figure in the picture to determine
the measure of each given angle.
Answers
Check the picture below.
.
The table shows the number of pools sold by the Allied Pool company over a six month period.
Allied Pool Sales
Month
Number of
Pools Sold
Feb.
11
Mar.
10
Apr.
12
May
16
June
15
July
18
According to the above table, what was the average number of pools sold per month during this period? Round to the nearest tenth if necessary.
Answers
According to the table, the average number of pools sold per month during this period is 14 (to the nearest tenth)
What is average?It is defined as the ratio of summation of all the data to the number of units present in the list. It can also be the middle value, calculated by dividing the total of all the values by the number of values.
The average can also be defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
It is represented mathematically as;
Average = Sum of Values/Number of Values
Average = total swimming pools sold in six months / number of months
Average = (11 + 10 + 12 + 16 + 15 + 18) / 6
Average = 82/6
Average = 13.7
Average = 14 (to the nearest tenth)
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The table at the right shows data representing a polynomial function. Answer A, B, and C.
Answers
a) The degree of the polynomial is 5.
b) The second difference is -726 -126 -6 114 714
c) The difference when they are constant is 480.
What is a polynomial?
A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.
y values: -999 -140 -7 0 1 116 945
1st difference 859 133 7 1 115 829
2nd difference -726 -126 -6 114 714
3rd difference 600 120 120 600
4th difference -480 0 480
5th difference 480 480
The degree of a polynomial is the number of difference where it is constant.
The degree of the polynomial function is 5.
The constant is the 5th difference which is 480.
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Evaluate fraction with negative 3 raised to the seventh power times negative 3 squared in the numerator and negative 3 raised to the fifth power in the denominator.
−81
−27
27
81
Answers
Answer:
Last option, 81.
Step-by-step explanation:
Evaluate, [tex]\frac{(-3)^{7}(-3)^{2} }{\ (-3)^{5} }[/tex]
[tex]\frac{(-3)^{7}(-3)^{2} }{\ (-3)^{5} }[/tex] => [tex]\frac{(-3)^{7+2} }{\ (-3)^{5} }[/tex] => [tex]\frac{(-3)^{9} }{\ (-3)^{5} }[/tex] => [tex](-3)^{9-5}[/tex] => [tex](-3)^{4}[/tex] => [tex](-3)(-3)(-3)(-3)[/tex] => [tex]81[/tex]
What do the properties of polynomial addition mean? Complete each statement.
The closure property states that the sum of two polynomials is a
The commutative property states that changing the order of two or more terms
~ the value of the sum.
The associative property states that the way in which two or more terms are grouped in a sum
the value.
Answers
The Complete statement are:
The closure property states that the sum of two polynomials is a polynomial.The commutative property states that changing the order of two or more terms does not change the value of the sum.The associative property states that the way in which two or more terms are grouped in a sum does not change the value of the sum.What is the properties of polynomial addition about?The properties of polynomial addition include closure, commutativity, and associativity.
These properties of polynomial addition make it easy to perform arithmetic operations with polynomials because they have predictable results and the order in which the polynomials are grouped or ordered does not change the final result.
Therefore, In simple terms, closure property ensures that the sum of two polynomials is also a polynomial, commutative property ensures that the order of the polynomials does not change the sum and the associative property ensures that the grouping of the polynomials does not change the sum.
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Answer:
Step-by-step explanation:
Please help will mark Brainly
Answers
Answer:
x=-1 and y=4
Step-by-step explanation:
When you draw a graph you will see point of intersection which is solution
A question on a test asks students to find the speed at which a car travels. The graph shows a proportional relationship between the distance traveled in miles and time in hours. billy incorrectly says that the speed of the car is 1/68 mile per hour. What is the speed of the car? What error might have billy made?
Answers
The car travels at the speed of 68 miles per hour.
Billy made error on substitution process.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
The graph shows a proportional relationship between the distance traveled in miles and time in hours.
That means,
distance traveled in miles/ time in hours = k,
where k is a proportional constant.
Here, k is the speed.
The incorrect speed is,
1/68 miles per hour.
k = 1/68.
From the graph,
distance = 272 miles
And the corresponding time is 4 hours.
So, the speed,
= distance / time
The speed = 272 / 4
The speed = 68 miles per hour.
Billy made the error of not substituting the right values to the formula.
Therefore, the speed of the car is 68 miles per hour.
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The complete question is given in the attached image.
Shaikha types at a rate of 34 words per minute. How many words does she type in 2 minutes?
Answers
Answer:
68 words
Step-by-step explanation:
If 34 words are typed in a minute what about two minutes hence take 34×2
Answer:
68
Step-by-step explanation:
What is a rate?A rate can be a quantity, or frequency, measured against a different quantity or amount.
If we know that Shaikha can type at a rate of 34 words per minute, and we need to figure out how many words she can type in 2 minutes, we can use an equation that looks like this:
Let m = minutes, w = words per minute and t = total words
m × w = t
Simply just insert your numbers into the equation.
2 × 34 = 68
Therefore, the number of words, or rate, that Shaikha types in 2 minutes is 68.